By Schuster A.

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**Extra resources for An Introduction to the Theory of Optics (2007)(en)(356s)**

**Example text**

As opposed to the earlier studies of collective excitations, the localised perturbations induced by the laser light correspond to a coherent superposition of many modes. The propagating wave packets were observed to disperse, as one might expect from either dephasing or damping of the modes. The actual variation of the density distribution should also come into play in certain limits and theoretical studies of such effects are underway (Zaremba, 1997; Kavoulakis and Pethick, 1997). S. F. 3. , excitation frequencies) of a trapped condensate.

The fugacity z is determined from the equation "g (z), where is the density, "(2 /Mk ¹) and " " g (z)" zI/k. S. F. Walls / Physics Reports 303 (1998) 1—80 Fig. 17. Spectra of light scattered from a Bose gas with various degrees of degeneracy. 3). 1 . From " Javanainen (1995). limit zP0, whereas Bose—Einstein statistics prevail where z"1. Frequency is measured in units of the effective Doppler width, "(k ¹" k"/M), for a temperature and scattering angle such " that the effective recoil frequency " " k"/2M" .

S. F. , collision terms of the form aL R aL aL R aL are neglected). At the time of an atom detection, the position at which the atom is detected is chosen using the conditional probability method of the previous section. So, after m atom detections at positions +x ,2, x , and times +t ,2, t ,, the state vector of the system will K K be of the form (143) 2" K (x )e\ &K RK\RK\ 2 K (x )e\ &K R " 2 . k2 , K I I with "c ""1. m#k) . " (146) (147) (148) The conditional probabilities are proportional to this expectation value; for non-zero collision rates ( O0), this value is a weighted sum over cosine functions with differing phase shifts, 4 kt.